Quantum measurement theory and its applications:
"Recent experimental advances in the control of quantum superconducting circuits, nano-mechanical resonators and photonic crystals has meant that quantum measurement theory is now an indispensable part of the modelling and design of experimental technologies. This book, aimed at graduate studen...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press
2014
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Cover Inhaltsverzeichnis |
| Zusammenfassung: | "Recent experimental advances in the control of quantum superconducting circuits, nano-mechanical resonators and photonic crystals has meant that quantum measurement theory is now an indispensable part of the modelling and design of experimental technologies. This book, aimed at graduate students and researchers in physics, gives a thorough introduction to the basic theory of quantum measurement and many of its important modern applications. Measurement and control is explicitly treated in superconducting circuits and optical and opto-mechanical systems, and methods for deriving the Hamiltonians of superconducting circuits are introduced in detail. Further applications covered include feedback control, metrology, open systems and thermal environments, Maxwell's demon, and the quantum-to-classical transition"-- |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XII, 544 S. graph. Darst. |
| ISBN: | 9781107025486 |
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| 520 | 1 | |a "Recent experimental advances in the control of quantum superconducting circuits, nano-mechanical resonators and photonic crystals has meant that quantum measurement theory is now an indispensable part of the modelling and design of experimental technologies. This book, aimed at graduate students and researchers in physics, gives a thorough introduction to the basic theory of quantum measurement and many of its important modern applications. Measurement and control is explicitly treated in superconducting circuits and optical and opto-mechanical systems, and methods for deriving the Hamiltonians of superconducting circuits are introduced in detail. Further applications covered include feedback control, metrology, open systems and thermal environments, Maxwell's demon, and the quantum-to-classical transition"-- | |
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Datensatz im Suchindex
| _version_ | 1804152460170756096 |
|---|---|
| adam_text | Contents
Preface
page
xi
1
Quantum
measurement theory
1
1.1
Introduction and overview
1
1.2
Classical measurement theory
4
1.2.1
Understanding
Bayes
theorem
6
1.2.2
Multiple measurements and Gaussian distributions
9
1.2.3
Prior states-of-knowledge and
invariance
11
1.3
Quantum measurement theory
15
1.3.1
The measurement postulate
15
1.3.2
Quantum states-of-knowledge: density matrices
15
1.3.3
Quantum measurements
20
1.4
Understanding quantum measurements
28
1.4.1
Relationship to classical measurements
28
1.4.2
Measurements of
observables
and resolving power
30
1.4.3
A measurement of position
31
1.4.4
The polar decomposition: bare measurements and feedback
34
1.5
Describing measurements within unitary evolution
37
1.6
Inefficient measurements
39
1.7
Measurements on ensembles of states
40
2
Useful concepts from information theory
48
2.1
Quantifying information
48
2.1.1
The entropy
48
2.1.2
The mutual information
53
2.2
Quantifying uncertainty about a quantum system
55
2.2.1
The
von
Neumann entropy
55
2.2.2
Majorization and density matrices
58
2.2.3
Ensembles corresponding to a density matrix
61
2.3
Quantum measurements and information
63
2.3.1
Information-theoretic properties
64
2.3.2
Quantifying disturbance
72
vu
viii Contents
2.4
Distinguishing quantum states
78
2.5
Fidelity of quantum operations
82
3
Continuous measurement
90
3.1
Continuous measurements with Gaussian noise
90
3.1.1
Classical continuous measurements
90
3.1.2
Gaussian quantum continuous measurements
96
3.1.3
When the
SME
is the classical Kalman-Bucy filter
104
3.1.4
The power spectrum of the measurement record
106
3.2
Solving for the evolution: the linear form of the
SME
113
3.2.1
The dynamics of measurement: diffusion gradients
117
3.2.2
Quantum jumps
119
3.2.3
Distinguishing quantum from classical
122
3.2.4
Continuous measurements on ensembles of systems
123
3.3
Measurements that count events: detecting photons
125
3.4
Homodyning: from counting to Gaussian noise
133
3.5
Continuous measurements with more exotic noise?
137
3.6
The
Heisenberg
picture: inputs, outputs, and spectra
137
3.7
Heisenberg-picture techniques for linear systems
145
3.7.1
Equations of motion for Gaussian states
145
3.7.2
Calculating the power spectrum of the measurement record
146
3.8
Parameter estimation: the hybrid master equation
150
3.8.1
An example: distinguishing two quantum states
152
4
Statistical mechanics, open systems, and measurement
160
4.1
Statistical mechanics
161
4.1.1
Thermodynamic entropy and the Boltzmann distribution
161
4.1.2
Entropy and information: Landauer s erasure principle
171
4.1.3
Thermodynamics with measurements: Maxwell s demon
175
4.2
Thermalization I: the origin of irreversibility
182
4.2.1
A new insight: the Boltzmann distribution from typicality
182
4.2.2
Hamiltonian typicality
185
4.3
Thermalization II: useful models
188
4.3.1
Weak damping
:
the Redfield master equation
189
4.3.2
Redfield equation for time-dependent or interacting systems
201
4.3.3
Baths and continuous measurements
202
4.3.4
Wavefunction Monte Carlo simulation methods
205
4.3.5
Strong damping
:
master equations and beyond
211
4.4
The quantum-to-classical transition
215
4.5
Irreversibility and the quantum measurement problem
222
5
Quantum feedback control
232
5.1
Introduction
232
5.2
Measurements versus coherent interactions
235
5.3
Explicit implementations of continuous-time feedback
239
Contents ix
5.3.1 Feedback
via continuous measurements
239
5.3.2
Coherent feedback via unitary interactions
242
5.3.3
Coherent feedback via one-way fields
243
5.3.4
Mixing one-way fields with unitary interactions:
a coherent version of Markovian feedback
247
5.4
Feedback control via continuous measurements
250
5.4.1
Rapid purification protocols
250
5.4.2
Control via measurement back-action
256
5.4.3
Near-optimal feedback control for a single qubit?
260
5.4.4
Summary
266
5.5
Optimization
266
5.5.1
Bellman s equation and the HJB equation
267
5.5.2
Optimal control for linear quantum systems
282
5.5.3
Optimal control for nonlinear quantum systems
290
6
Metrology
303
6.1
Metrology of single quantities
304
6.1.1
The Cramer-Rao bound
304
6.1.2
Optimizing the Cramer-Rao bound
305
6.1.3
Resources and limits to precision
307
6.1.4
Adaptive measurements
309
6.2
Metrology of signals
311
6.2.1
Quantum-mechanics-free subsystems
312
6.2.2
Oscillator-mediated force detection
314
7
Quantum mesoscopic systems I: circuits and measurements
323
7.1
Superconducting circuits
323
7.1.1
Procedure for obtaining the circuit Lagrangian (short method)
329
7.2
Resonance and the rotating-wave approximation
330
7.3
Superconducting harmonic oscillators
334
7.4
Superconducting nonlinear oscillators and qubits
336
7.4.1
The
Josephson
junction
336
7.4.2
The Cooper-pair box and the transmon
340
7.4.3
Coupling qubits to resonators
343
7.4.4
The RF-SQUID and flux qubits
344
7.5
Electromechanical systems
346
7.6
Optomechanical systems
351
7.7
Measuring mesoscopic systems
354
7.7.1
Amplifiers and continuous measurements
354
7.7.2
Translating between experiment and theory
361
7.7.3
Implementing a continuous measurement
361
7.7.4
Quantum transducers and nonlinear measurements
370
8
Quantum mesoscopic systems II: measurement and control
383
8.1
Open-loop control
383
χ
Contents
8.1.1
Fast state-swapping for oscillators
387
8.1.2
Preparing non-classical states
389
8.2
Measurement-based feedback control
396
8.2.1
Cooling using linear feedback control
397
8.2.2
Squeezing using linear feedback control
404
8.3
Coherent feedback control
408
8.3.1
The resolved-sideband cooling method
408
8.3.2
Resolved-sideband cooling via one-way fields
412
8.3.3
Optimal cooling and state-preparation
416
Appendix A The tensor product and partial trace
432
Appendix
В
A fast-track introduction for experimentalists
441
Appendix
С
A quick introduction to ho calculus
448
Appendix
D
Operators for qubits and modes
451
Appendix
E
Dictionary of measurements
456
Appendix
F
Input-output theory
458
F.I A mode of an optical or electrical cavity
458
F.2 The traveling-wave fields atx =
0:
the input and output signals
462
F.3 The
Heisenberg
equations of motion for the system
463
FA A weakly damped oscillator
467
F.5 Sign conventions for input-output theory
467
F.6 The quantum noise equations for the system:
Ito
calculus
468
F.7 Obtaining the Redfield master equation
469
F.8 Spectrum of the measurement signal
470
Appendix
G
Various formulae and techniques
475
G. I The relationship between Hz and s~1
,
and writing decay rates in Hz
475
G.2 Position representation of a pure Gaussian state
475
G.3 The multivariate Gaussian distribution
476
G.4 The rotating-wave approximation
(RWA) Alb
G.5 Suppression of off-resonant transitions
477
G.6 Recursion relations for time-independent perturbation theory
478
G.
7
Finding operator transformation, reordering, and splitting relations
479
G.8 The
Haar
measure
484
G.9 General form of the Kushner-Stratonovich equation
485
GAO
Obtaining steady states for linear open systems
486
Appendix
H
Some proofs and derivations
490
H.I The Schumacher-Westmoreland-Wootters theorem
490
Ή.2
The operator-sum representation for quantum evolution
492
H.3 Derivation of the Wiseman-Milburn Markovian feedback
SME
494
References
498
Index
539
|
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| spelling | Jacobs, Kurt Verfasser (DE-588)140929134 aut Quantum measurement theory and its applications Kurt Jacobs 1. publ. Cambridge Cambridge Univ. Press 2014 XII, 544 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index "Recent experimental advances in the control of quantum superconducting circuits, nano-mechanical resonators and photonic crystals has meant that quantum measurement theory is now an indispensable part of the modelling and design of experimental technologies. This book, aimed at graduate students and researchers in physics, gives a thorough introduction to the basic theory of quantum measurement and many of its important modern applications. Measurement and control is explicitly treated in superconducting circuits and optical and opto-mechanical systems, and methods for deriving the Hamiltonians of superconducting circuits are introduced in detail. Further applications covered include feedback control, metrology, open systems and thermal environments, Maxwell's demon, and the quantum-to-classical transition"-- Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenmechanisches System (DE-588)4300046-0 gnd rswk-swf Messprozess (DE-588)4169530-6 gnd rswk-swf Messung (DE-588)4038852-9 gnd rswk-swf Messprozess (DE-588)4169530-6 s Quantenmechanik (DE-588)4047989-4 s DE-604 Quantenmechanisches System (DE-588)4300046-0 s Messung (DE-588)4038852-9 s http://assets.cambridge.org/97811070/25486/cover/9781107025486.jpg Cover Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027477588&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jacobs, Kurt Quantum measurement theory and its applications Quantenmechanik (DE-588)4047989-4 gnd Quantenmechanisches System (DE-588)4300046-0 gnd Messprozess (DE-588)4169530-6 gnd Messung (DE-588)4038852-9 gnd |
| subject_GND | (DE-588)4047989-4 (DE-588)4300046-0 (DE-588)4169530-6 (DE-588)4038852-9 |
| title | Quantum measurement theory and its applications |
| title_auth | Quantum measurement theory and its applications |
| title_exact_search | Quantum measurement theory and its applications |
| title_full | Quantum measurement theory and its applications Kurt Jacobs |
| title_fullStr | Quantum measurement theory and its applications Kurt Jacobs |
| title_full_unstemmed | Quantum measurement theory and its applications Kurt Jacobs |
| title_short | Quantum measurement theory and its applications |
| title_sort | quantum measurement theory and its applications |
| topic | Quantenmechanik (DE-588)4047989-4 gnd Quantenmechanisches System (DE-588)4300046-0 gnd Messprozess (DE-588)4169530-6 gnd Messung (DE-588)4038852-9 gnd |
| topic_facet | Quantenmechanik Quantenmechanisches System Messprozess Messung |
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